A sinking fund was set up with level half-yearly deposits to redeem a loan of $1,000,000 in 10 years time based on a fund earning rate of 11% p.a. compounded semi-annually. After 4 years the fund earning rate increased to 12% p.a. compounded quarterly.

a) assuming that the size of the deposits remained unchanged, how much extra money will there be at the end of the 10 years?

b) by how much could the half-yearly deposits have been reduced, in view of the rise in the earning interest rate?